Rule: Q[1, 12]

Type

This rule is of Legendre type.

Polynomials

One starts from the polynomial $P_{1}$ and extends one by one with $P_{i}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

$P_{1}$ :
$t$
$P_{2}$ :
$t^{13} - \frac{78}{25} \cdot t^{11} + \frac{429}{115} \cdot t^{9} - \frac{1716}{805} \cdot t^{7} + \frac{1287}{2185} \cdot t^{5} - \frac{2574}{37145} \cdot t^{3} + \frac{429}{185725} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98418305471858814947 + 4.3962742470575570919e-211j	1.84e-60, 1.84e-60j
-0.98418305471858814947 - 4.3767806323641008632e-212j	1.62e-60, 1.62e-60j
-0.91759839922297796521 - 8.4936464021487853443e-213j	3.27e-60, 3.27e-60j
-0.23045831595513479407 + 4.1019627273014060027e-216j	5.5e-63, 5.5e-63j
0.64234933944034022064 - 6.3818381436910272396e-215j	5.28e-61, 5.28e-61j
0.80157809073330991279 + 4.1430390115181673197e-218j	1.98e-60, 1.98e-60j
-7.9967762704792350485e-223 - 7.3483890053052430175e-223j	1.41e-221, 1.41e-221j
-0.80157809073330991279 + 1.0158067154392541818e-222j	1.71e-60, 1.71e-60j
-0.64234933944034022064 - 1.5136699608553263274e-230j	5.58e-61, 5.58e-61j
0.23045831595513479407 - 9.9819819932893196353e-238j	5.77e-63, 5.77e-63j
0.91759839922297796521 - 2.6689916734798807149e-240j	2.82e-60, 2.82e-60j
0.44849275103644685288 - 3.1893958043930597584e-245j	6.96e-62, 6.96e-62j
-0.44849275103644685288 + 1.3855278858770298838e-247j	7.7e-62, 7.7e-62j

Weights

Weight (ball center)	Error (ball radius)
0.04048400476531587952 - 5.589106932255106627e-211j	1.43e-19, 9.3e-49j
0.04048400476531587952 - 6.8080458854874616796e-212j	6.26e-20, 4.06e-49j
0.092121499837728447914 + 1.1720894802216464619e-211j	5.11e-20, 3.31e-49j
0.22628318026289723841 + 2.1646258949669137962e-211j	1.03e-20, 6.69e-50j
0.17814598076194573828 + 4.8106327878233560322e-211j	6.41e-21, 4.16e-50j
0.13887351021978723846 - 6.1455924325975974316e-211j	4.45e-21, 2.89e-50j
0.23255155323087391019 - 2.65636800613827709e-211j	4.47e-21, 2.9e-50j
0.13887351021978723846 - 1.1050378842052551675e-211j	2.01e-21, 1.31e-50j
0.17814598076194573828 + 1.3872981301047019599e-211j	1.22e-21, 7.92e-51j
0.22628318026289723841 + 3.2301667964218671145e-211j	4.5e-22, 2.97e-51j
0.092121499837728447914 + 9.0745943007652426576e-211j	7.06e-23, 4.62e-52j
0.20781604753688850231 - 3.920597715368362184e-211j	1.53e-22, 1.01e-51j
0.20781604753688850231 - 1.7418998311903833541e-211j	1.22e-22, 7.04e-52j

Download

All rules of Legendre type can be downloaded here packed into a single file.